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Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers The variance of road octane number for formulation 1 is 2 15, and for 1 2 formulation 2 it is 2 12 Two random samples of size n1 15 and n2 20 are tested, and the mean road octane numbers observed are x1 896 and x2 925 Assume normality (a) Construct a 95% two-sided con dence interval on the difference in mean road octane number (b) If formulation 2 produces a higher road octane number than formulation 1, the manufacturer would like to detect.

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col.DataField = hire_date col.DataFormatString = {0:d} col.ItemStyle.HorizontalAlign = HorizontalAlign.Right col.HeaderStyle.HorizontalAlign = HorizontalAlign.Center col.ItemStyle.Width = New Unit(colWidth, UnitType.Pixel) dgEmployee.Columns.Add(col) dgEmployee.Attributes(col.DataField) = _ dgEmployee.Columns.Count - 1 col = New BoundColumn() col.HeaderText = Job<BR>ID col.DataField = job_id col.ItemStyle.HorizontalAlign = HorizontalAlign.Right col.HeaderStyle.HorizontalAlign = HorizontalAlign.Center col.ItemStyle.Width = New Unit(colWidth, UnitType.Pixel) dgEmployee.Columns.Add(col) dgEmployee.Attributes(col.DataField) = _ dgEmployee.Columns.Count - 1 col = New BoundColumn() col.HeaderText = Job<BR>Level col.DataField = job_lvl col.ItemStyle.HorizontalAlign = HorizontalAlign.Right col.HeaderStyle.HorizontalAlign = HorizontalAlign.Center col.ItemStyle.Width = New Unit(colWidth, UnitType.Pixel) dgEmployee.Columns.Add(col) dgEmployee.Attributes(col.DataField) = _ dgEmployee.Columns.Count - 1 End Sub

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(a) Do you think the engineer is correct Use 0.05. (b) What is the P-value for this test (c) What is the power of the test in part (a) for a true difference in means of 0.04 (d) Find a 95% con dence interval on the difference in means. Provide a practical interpretation of this interval. (e) Assuming equal sample sizes, what sample size should be used to assure that 0.05 if the true difference in means is 0.04 Assume that 0.05. 10-2. Two types of plastic are suitable for use by an electronics component manufacturer. The breaking strength of this plastic is important. It is known that 1 1.0 psi. From 2 a random sample of size n1 10 and n2 12, we obtain x1 162.5 and x2 155.0 . The company will not adopt plastic 1 unless its mean breaking strength exceeds that of plastic 2 by at least 10 psi. Based on the sample information, should it use plastic 1 Use 0.05 in reaching a decision. 10-3. Reconsider the situation in Exercise 10-2. Suppose that the true difference in means is really 12 psi. Find the power of the test assuming that 0.05. If it is really important to detect this difference, are the sample sizes employed in Exercise 10-2 adequate, in your opinion 10-4. The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning rate; that is 1 3 2 centimeters per second. Two random samples of n1 20

it Formulate and test an appropriate hypothesis, using 005 (c) What is the P-value for the test you conducted in part (b) 10-8 Consider the situation described in Exercise 10-4 What sample size would be required in each population if we wanted the error in estimating the difference in mean burning rates to be less than 4 centimeters per second with 99% con dence 10-9 Consider the road octane test situation described in Exercise 10-7 What sample size would be required in each population if we wanted to be 95% con dent that the error in estimating the difference in mean road octane number is less than 1 10-10 A polymer is manufactured in a batch chemical process Viscosity measurements are normally made on each batch, and long experience with the process has indicated that the variability in the process is fairly stable with 20.

The DataGrid can be used to edit a DataRow by setting the EditItemIndex property of the DataGrid to the item number to be edited (see Figure 8.9). In addition, canceling the edit must set the EditItemIndex to -1. The following code shows the implementation.

Fifteen batch viscosity measurements are given as follows: 724, 718, 776, 760, 745, 759, 795, 756, 742, 740, 761, 749, 739, 747, 742 A process change is made which involves switching the type of catalyst used in the process Following the process change, eight batch viscosity measurements are taken: 735, 775, 729, 755, 783, 760, 738, 780 Assume that process variability is unaffected by the catalyst change Find a 90% con dence interval on the difference in mean batch viscosity resulting from the process change 10-11 The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in the process The standard deviation of active concentration is known to be 3 grams per liter, regardless of the catalyst type Ten observations on concentration are taken with each catalyst, and the data follow: Catalyst 1: 579, 662, 65.

4, 654, 652, 626, 676, 637, 672, 710 Catalyst 2: 664, 717, 703, 693, 648, 696, 686, 694, 653, 688.

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